{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.4 常见问题及对策"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "学完多层感知机，知道了什么是前向传播、反向传播，其实你已经窥见了深度学习的精髓。为什么这么说呢？因为整个深度学习后面所涉及的内容其实全是在这个基础上发展起来的。说白了，都没有离开这个小圈圈。那咱们为啥还要学后面那么多章节内容呢？原因啊，就在于实际情况千奇百怪十分复杂，远不是简单的多层感知机就能解决好的。因此，想学好更复杂的深层神经网络知识，先要明确要解决的问题是什么。各种看似高级的技术，其实只不过在不停解决各种问题。本节咱们就来看数据和模型匹配方面的常见问题。先来看看模型复杂度。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.1 模型复杂度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "有了多层感知机这样的神经网络，你有没有好奇到底该怎么决定网络结构啊？该用多少层，每层用多少个神经元，是越多越好吗？选择的原则是什么？这些问题就涉及到了模型复杂度，也就是神经网络的复杂程度。模型复杂度指的是模型的表示能力，即模型可以拟合的数据的复杂度程度。模型复杂度越高，模型就能表示的数据就越复杂，但同时也会增加过拟合的风险。\n",
    "\n",
    "在深度学习中，模型复杂度主要取决于网络的层数和神经元数量。随着网络层数的增加或神经元数量的增加，模型的复杂度也会增加。当模型复杂度过高时，模型容易过拟合训练数据，导致在测试数据上的表现不佳。因此，在训练深度学习模型时，需要适当控制模型的复杂度，以避免过拟合问题。常用的方法包括使用正则化技术（如 L1 和 L2 正则化）、使用 K 折交叉验证选择最佳模型、使用数据增强技术等。此外，还可以通过减小网络层数或神经元数量、使用 dropout 等方法来限制模型的复杂度。\n",
    "\n",
    "这里面一下子提到了不少新词：过拟合、正则化、K折交叉验证、数据增强、dropout等，看不懂别捉急，咱们一个个讲清楚。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.2 过拟合问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "过拟合是指在训练深度学习模型时，模型在训练数据上表现良好，但在测试数据上表现不佳的情况。这意味着模型对训练数据进行了过度拟合，从而无法适用于真实世界中的数据。\n",
    "\n",
    "过拟合通常是由模型复杂度过高导致的。当模型复杂度增加时，它可以更好地拟合训练数据中的噪声和细节。但是，这同时也会使模型对真实世界中的数据过度拟合，因此表现不佳。\n",
    "\n",
    "为了避免过拟合，可以使用正则化技术来限制模型的复杂度。常用的正则化技术包括 L1 和 L2 正则化。这些技术通过在损失函数中添加惩罚项来减少模型的复杂度。此外，还可以通过使用更少的训练数据、减小网络层数或神经元数量、使用 dropout 等方法来防止过拟合。\n",
    "\n",
    "在实际应用中，过拟合是一个常见问题，因此需要通过合适的方法来避免。过拟合不仅会导致模型在测试数据上的表现不佳，还会使模型对真实世界中的数据不具有泛化能力，因此需要谨慎对待。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.3 欠拟合问题"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "欠拟合是指在训练深度学习模型时，模型在训练数据上的表现不佳，即模型没有很好地拟合训练数据。这意味着模型的复杂度过低，无法很好地捕捉数据中的特征。\n",
    "\n",
    "欠拟合常常是由模型复杂度过低导致的。当模型复杂度过低时，它无法很好地拟合训练数据中的细节和特征。因此，模型在训练数据上的表现不佳。\n",
    "\n",
    "为了避免欠拟合，可以通过增加模型的复杂度来提高模型的表示能力。常用的方法包括增加网络层数或神经元数量、使用更复杂的模型结构（如卷积神经网络或循环神经网络）等。此外，还可以使用数据增强技术来增加训练数据的数量和多样性，从而提高模型的泛化能力。正确地处理欠拟合问题可以提高模型的性能和泛化能力。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.4 相互关系\n",
    "\n",
    "模型复杂度、过拟合、欠拟合三者之间存在一定依存关联，下面这张图能清晰表达此消彼长的关系。\n",
    "\n",
    "<img src=\"../images/5-4-1.png\" width=\"40%\"></img>\n",
    "\n",
    "中间是最佳分界线，横轴是模型复杂度，越往右我们可以看出越容易过拟合，越往左越容易欠拟合。模型越复杂，训练误差越小，这很容易理解。但是泛化误差就不一定了，无论过拟合，还是欠拟合都不好，两种情况下泛化误差，也就是测试误差都会变大。只有在中间线这个地方泛化误差最小，因此这就是我们模型选择的目标了。\n",
    "\n",
    "这里涉及到的训练误差和泛化误差两个概念，稍微多说两句。\n",
    "\n",
    "在训练深度学习模型时，泛化误差指的是模型在真实世界中的数据上的误差。泛化误差是我们最终关心的误差，因为它反映了模型对真实世界数据的预测能力。训练误差指的是模型在训练数据上的误差。训练误差可以作为训练过程中的一个指标，但最终我们关心的是模型的泛化能力，即在真实世界中的数据上的表现。在训练时，通常会使用训练数据和测试数据来评估模型的性能。训练数据用于训练模型，测试数据用于评估模型的泛化能力。如果模型在训练数据上表现良好，但在测试数据上表现不佳，则可能存在过拟合问题。\n",
    "\n",
    "举个例子，假设我们要建立一个机器学习模型来预测房屋价格。我们收集了一些历史房屋交易数据，并用这些数据来训练模型。这些数据就是我们的训练数据。在训练过程中，我们希望模型能够准确地拟合训练数据，也就是希望训练误差尽可能小。但是，我们也希望模型能够很好地适用于新数据，也就是说，希望模型的泛化误差尽可能小。\n",
    "\n",
    "在实际应用中，我们通常希望泛化误差尽可能小，因为这意味着模型能够很好地适用于新数据。但是，训练误差和泛化误差之间通常存在一定的关系，即训练误差越小，泛化误差就越小。但是，如果训练误差过小，模型就可能出现过拟合的情况，即模型过于复杂，只能很好地拟合训练数据，但是对新数据的预测能力较差。因此，在训练机器学习模型时，我们需要尽量减小泛化误差，同时避免过拟合的情况。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.5 应对策略\n",
    "面对一不小心就过拟合、欠拟合这些问题，怎么办呢？可以从数据复杂度、模型复杂度、训练策略三方面下手。与之对应的就是数据集大小选择、数据增强、增加验证集；模型选择、K折交叉验证；正则化、dropout方法了。咱们分别来看看。\n",
    "\n",
    "#### 数据集大小选择\n",
    "\n",
    "在训练深度学习模型时，数据集的大小可能会对过拟合问题产生影响。通常来说，如果数据集较小，模型很容易就会出现过拟合的情况。因为在较小的数据集上，模型很容易就能够很好地拟合训练数据，但是在新数据上的表现却很差。这是因为模型在训练过程中学习到的特征可能只针对训练数据有效，对新数据并没有太大的意义。\n",
    "\n",
    "相反，如果数据集较大，模型很难出现过拟合的情况。这是因为在较大的数据集上，模型有更多的数据可以学习，因此模型很难将训练数据完全拟合。这样，模型就可以学习到更加泛化的特征，对新数据的表现就会更好。然而，数据集过大也可能导致模型的训练效率降低。因此，我们在选择数据集大小时，需要权衡这些因素，并选择合适的数据集大小。\n",
    "\n",
    "#### 数据增强是什么\n",
    "\n",
    "在训练深度学习模型时，数据增强是指通过对训练数据进行变换，以增加训练数据的数量和多样性的一种技术。数据增强通常是通过对训练数据进行旋转、翻转、剪切、改变亮度等操作来实现的。\n",
    "\n",
    "使用数据增强可以有效解决过拟合问题。同时，使用数据增强还可以提高模型在新数据上的泛化能力。因为通过数据增强生成的新数据可以更好地代表真实数据的分布，因此模型在新数据上的表现也会更好。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 为什么要用验证集\n",
    "\n",
    "在训练深度学习模型时，通常会使用训练集、验证集和测试集进行模型训练和评估。其中，训练集用于训练模型，测试集用于最终评估模型的性能，而验证集则是辅助模型选择和调参的一种工具。\n",
    "\n",
    "使用验证集的好处在于，我们可以在训练过程中就对模型进行评估，而不需要等到训练结束才进行评估。这样，我们就可以及时发现模型的问题，并可以及时调整模型的超参数或模型结构。同时，使用验证集进行模型评估可以避免测试集的偏差，从而使得模型的评估更加准确。\n",
    "\n",
    "假设我们要训练一个深度学习模型来进行图像分类。我们收集了一些图像数据，共有1000张图片，将这些图片分为训练集、验证集和测试集，每个集合各占图片总数的60%、20%和20%。\n",
    "\n",
    "首先，我们使用训练集来训练模型。我们设定了两种不同的模型，分别是模型A和模型B。在训练过程中，我们使用验证集来评估模型的性能。我们发现，模型A在验证集上的性能略优于模型B。因此，我们决定选择模型A进行进一步训练。\n",
    "\n",
    "在进一步训练模型A的过程中，我们发现模型A的训练误差逐渐降低，但是验证集上的误差却逐渐升高。这种情况通常是由于模型A出现了过拟合的情况。因此，我们决定停止模型A的训练，并使用最终训练好的模型A来在测试集上进行评估。\n",
    "\n",
    "最终，我们使用测试集评估模型A的性能，发现模型A的性能较优。因此，我们选择使用模型A来进行实际的图像分类任务。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 模型选择\n",
    "\n",
    "在训练深度学习模型时，模型选择是很重要的一环。模型选择的好坏直接影响到模型的性能，因此选择合适的模型是很重要的。\n",
    "\n",
    "常用的模型选择方法有以下几种：\n",
    "\n",
    "1. 网格搜索：通过对模型的超参数进行网格搜索，找到最优的超参数组合。\n",
    "2. 随机搜索：随机选择模型的超参数进行搜索，找到最优超参数。\n",
    "3. 交叉验证：将训练数据分为训练集和验证集，利用验证集来选择最优的模型。\n",
    "4. 集成方法：利用多个模型的输出结果进行集成，得到最终的模型。\n",
    "\n",
    "在选择模型时，还需要考虑模型的泛化能力、训练时间、模型复杂度、计算资源、预测效率等因素。因此，选择合适的模型是很重要的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### K折交叉验证\n",
    "\n",
    "K 折交叉验证（K-fold cross-validation）是一种在机器学习中常用的评估模型性能的方法。它的基本思想是将训练数据划分为 K 份，然后进行 K 次训练和验证。K 折交叉验证在深度学习中也是常用的方法。它可以有效评估模型的性能，并且可以在训练过程中发现模型的过拟合情况。\n",
    "\n",
    "使用 K 折交叉验证的步骤如下：\n",
    "\n",
    "1. 将训练数据划分为 K 份。\n",
    "2. 对于每一份数据，将其作为验证集，剩余的 K-1 份数据作为训练集，进行训练和验证。\n",
    "3. 计算 K 次验证的平均值。\n",
    "\n",
    "K 折交叉验证的优点是可以充分利用训练数据，提高模型的泛化能力。但是，它的计算时间较长，因此在实际应用中需要权衡时间和精度的折中。\n",
    "\n",
    "**梗直哥提示：我们看到模型选择、验证集使用和K折交叉验证几个策略息息相关，如果你对这方面的知识不是很熟悉，欢迎补足，来听听过来人怎么说。[“解一卷而众篇明”之机器学习核心概念精讲](https://aay.xet.tech/s/2TMAev)**\n",
    "\n",
    "正则化和dropout稍微复杂些，咱们下面两节单独讲。这里先来看个过拟合的实际例子，感受一下。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4.6 代码示例\n",
    "\n",
    "为了让大家有更加感性的认知，我们用一个 PyTorch 的例子，演示不同模型情况下欠拟合、正常和过拟合三种情况，并可视化训练和测试误差。\n",
    "\n",
    "首先，导入所需库，并用 PyTorch 的 torch.utils.data.DataLoader 类来生成一些虚拟数据。这些数据将满足一个线性方程 $ y = x^2 + 1 $，但是我们将会增加一些噪声来使它不完全符合这个方程。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "np.random.seed(32)\n",
    "\n",
    "# 生成满足 y = x^2 + 1 的数据\n",
    "num_samples = 100\n",
    "X = np.random.uniform(-5, 5, (num_samples, 1))\n",
    "Y = X ** 2 + 1 + 5 * np.random.normal(0, 1, (num_samples, 1))\n",
    "\n",
    "# 将 NumPy 变量转化为浮点型 PyTorch 变量\n",
    "X = torch.from_numpy(X).float()\n",
    "Y = torch.from_numpy(Y).float()\n",
    "\n",
    "# 绘制数据点\n",
    "plt.scatter(X, Y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 将数据拆分为训练集和测试集\n",
    "train_X, test_X, train_Y, test_Y = train_test_split(X, Y, test_size=0.3, random_state=0)\n",
    "\n",
    "# 将数据封装成数据加载器\n",
    "train_dataloader = DataLoader(TensorDataset(train_X, train_Y), batch_size=32, shuffle=True)\n",
    "test_dataloader = DataLoader(TensorDataset(test_X, test_Y), batch_size=32, shuffle=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来，定义三种不同的模型，分别演示欠拟合、正常和过拟合三种情况。\n",
    "\n",
    "欠拟合可以使用一个线性回归模型，但是输入维度为 1，输出维度也为 1。因为线性回归模型没有隐藏层，所以它可能无法很好地拟合复杂的数据。\n",
    "\n",
    "正常情况使用一个包含一个隐藏层的多层感知机（MLP）。这个模型的输入维度仍为 1，输出维度也为 1。\n",
    "\n",
    "过拟合用一个比上述模型更复杂的 MLP，它具有更多的隐藏层和更多的隐藏单元。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义线性回归模型（欠拟合）\n",
    "class LinearRegression(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.linear = nn.Linear(1, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.linear(x)\n",
    "\n",
    "# 定义多层感知机（正常）\n",
    "class MLP(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.hidden = nn.Linear(1, 8)\n",
    "        self.output = nn.Linear(8, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.hidden(x))\n",
    "        return self.output(x)\n",
    "\n",
    "# 定义更复杂的多层感知机（过拟合）\n",
    "class MLPOverfitting(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.hidden1 = nn.Linear(1, 256)\n",
    "        self.hidden2 = nn.Linear(256, 256)\n",
    "        self.output = nn.Linear(256, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.hidden1(x))\n",
    "        x = torch.relu(self.hidden2(x))\n",
    "        return self.output(x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来，我们可以使用这三种模型来训练模型并计算训练和测试误差。为了计算误差，我们可以使用均方误差（MSE）作为损失函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_errors(models, num_epochs, train_dataloader, test_dataloader):\n",
    "    # 定义损失函数\n",
    "    loss_fn = nn.MSELoss()\n",
    "\n",
    "    # 定义训练和测试误差数组\n",
    "    train_losses = []\n",
    "    test_losses = []\n",
    "\n",
    "    # 迭代训练\n",
    "    for model in models:\n",
    "        # 初始化模型和优化器\n",
    "        optimizer = torch.optim.SGD(model.parameters(), lr=0.01)\n",
    "\n",
    "        train_losses_per_model = []\n",
    "        test_losses_per_model = []\n",
    "        for epoch in range(num_epochs):\n",
    "            # 在训练数据上迭代\n",
    "            model.train()\n",
    "            train_loss = 0\n",
    "            for inputs, targets in train_dataloader:\n",
    "                optimizer.zero_grad()\n",
    "                outputs = model(inputs)\n",
    "                loss = loss_fn(outputs, targets)\n",
    "                loss.backward()\n",
    "                optimizer.step()\n",
    "                train_loss += loss.item()\n",
    "            train_loss /= len(train_dataloader)\n",
    "            train_losses_per_model.append(train_loss)\n",
    "\n",
    "            # 在测试数据上评估\n",
    "            model.eval()\n",
    "            test_loss = 0\n",
    "            with torch.no_grad():\n",
    "                for inputs, targets in test_dataloader:\n",
    "                    outputs = model(inputs)\n",
    "                    loss = loss_fn(outputs, targets)\n",
    "                    test_loss += loss.item()\n",
    "                test_loss /= len(test_dataloader)\n",
    "                test_losses_per_model.append(test_loss)\n",
    "\n",
    "        train_losses.append(train_losses_per_model)\n",
    "        test_losses.append(test_losses_per_model)\n",
    "\n",
    "    return train_losses, test_losses\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后，我们可以使用 Matplotlib 绘制训练和测试误差曲线，以便我们可以清楚地看到三种模型的变化趋势。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sscdSUlICwKxZs9i6dSsNDQ0ceeSRlJeXm8f97LPPMnpcAwNR7scBa6WU5kSFQogqoElKGRVCTAGmApsG2Ma0kKpwWFhX7IaCt2Ej63HyLZnfZ8N6VVsmTUgpmT17dtJiXc888wxvvPEGTz31FD/72c9YtSq9XsbixYtZtWoV+fn5TJs2La1tDM/dilmzZrFs2TLOPPNMc9myZctM4j/jjDO48cYbaWpqYtmyZRxzzDF0dHRQWlqatGYLMCglfvtS+ngwkE4q5APAu8B0IUSdEOKr+kcXEG/JABwBfKynRj4KXCGlbMpge/uMqE7qmk3uNmykDa/XS319vUnu4XCYNWvWoGka27dv5+ijj+aXv/wlra2ttLe3p13q9pZbbklLsfcEo/67QdSNjY18//vfN33twsJCDjzwQP7nf/6H0047DafTSXFxMZMnT+aRRx4B1MNr5cqVfT622+02JynpT3nfAw88kNdff53m5mYikUjSmawyhXSyZZJObCilvDTJssdQqZHDCmuly0jUDqjasBGLREnSGc3tcDh49NFHueaaa2htbSUSiXDttdcybdo0vvCFL9Da2oqUkmuuuYbS0lJOP/10zj33XP7zn/9w++23s2RJ8lyKk08+OeUxTz31VHM6vkMOOcScFi8RY8aM4V//+heXXXYZfr8fKSXXXnstp59+urnO+eefz3nnnWdOiQdqko8rr7yS//3f/yUcDnPBBRf02e++/PLLmTdvHgsWLOD+++/nsMMOY86cOZx88skp22tFTU0NN954I4sXL6a8vJwZM2aY1k2mkfslfxs3wu0LuCNyBt9wPclVoWs46+JvcMLsagBW1bVy+h/f4pJDJvLjM+dksNU2bGQOg17yt+EzCHVA9QHg2CcGpmct2tvbKSwsJBKJcPbZZ/OVr3yFs88+u9ft+lryd8T/yobnbgdUbezTkN1e2Bgm3HzzzdTW1jJnzhwmT57cp6B0XzAiS/5aETVTIe2L2sa+DPv6zxbceuutQ3KcEafcBQl57lGb3G3kBobGIrXvg1xEf66NEUPuqVIhDVK3UyFtZDN8Ph+NjY2DT/D2bZBzkFLS2NiIz+fr03Y5b8u8vaGBw3r43PDc7VRIG9mMcePGUVdXR319/eAcwL8boiFoXguOzA7WsTH48Pl8jBs3rk/b5Dy5f7StpUdyj41QHZr22LDRH7jdbiZPnjx4B/jL12HXSvjuBiisGrzj2Mga5LwtU9fc0W2ZtWdr15axYQOQWvx/GyMeOU/u25s7ky7f2dJFVJOWkr+S215ez9rd3WqY2bAx8mGOYbLJfV9BzpP7zpYAEB9QbesKc9SvX+PZ1bvMgGowovHbFz/j2VW7h6WdNmwMK0zlbk83ua8gp8ndH+g+u5JA0toVJhTV2N0aMFMhg2E9sGoPZrKxT0K/7m3lvs8gp8l9w95YlTsrZQfCSp20ByMW5a6W2SmRNvZJ2J77PoecJvf9RhXy/ZNmdFsejKgLuDMUNVMhjWX2YCYb+yRsct/nkNPkXuxzc9j+Fd2WGyq9I0652+RuYx+GYUfaWWP7DHKa3AGcSWaVsSp303PXCd8mdxv7JGzlvs8h98nd0Z3crZ67kQppBFQjtnKxsU/CDqjua8h9ck9SUiYQNpR7xAygxmyZIWuaDRvZA1u573PIfXLXlbs1zz3muUfN8gMxW8a+uG3sg7Dz3Pc55Dy5iwTPXSBNld4R7K7c7VRIG/sk7BGq+xzSmSD7HiHEXiHEasuym4UQO4QQK/S/Uyyf3SCE2CCEWCeEOHGwGp6kpearYNgSUNWVupEsYAdUbeyTsG2ZfQ7pKPd7gZOSLP+dlLJW//svgBBiFnABMFvf5k9CiMGrL9rRCB8/1G1xwLBlLJ67AZvcbeybsAOq+xp6JXcp5RtAU5r7OxN4UEoZlFJuBjYAiwfQvp7RsgXe+HW3xWZA1eK5G7DJ3cY+CVO529f/voKBeO7fFEJ8rNs2ZfqyGmC7ZZ06fVk3CCEuF0IsFUIs7fcEBSk6BUbwNBTV6AzHB5Bsz93GPgmD3LV9IKBatxSW/3O4W6Fw2wJY/o9hOXR/yf3PwH5ALbAL+E1fdyClvEtKuUhKuaiqqp+TBziSzzVieO6gKkRaYc/IZGOfhMxSW+ajf0HD+szuc/k/4OWfZHaf/UXTRmjeMiyH7he5Syn3SCmjUkoN+Csx62UHMN6y6jh92eAgxXRhhnIHaAtE4j6zlbuNfRLZGlB9+luw4v7M7lNGs+M8h/mB2i9yF0KMsbw9GzAyaZ4ELhBCeIUQk4GpwAcDa2IPsCj3kFSvvSIcp9xbE5S77bnb2DeRpcpdi6i/jO5Ty458fsMCGyYrrNc5VIUQDwBHAZVCiDrgJuAoIUQt6orZAnwdQEq5RgjxMPAJEAG+IeUgfssi9myqpwSAKlrNnHbobsvY5Qds7JPIxkFMUqp2ZZr8pJYdD7Fh7i31Su5SyguTLL67h/V/BvxsII1KGxZbpkt6CTgLGRVpJtQDudvcbmOfRDbaMmalykyTezQ7soKG+TvP7RGqCQHVdnclo0UzECtLkGjL2Mrdxj6JbByhavQiMm3LDEZvoL/tsP4fYuQ2uSekQrZ7qkxyL8t3A90DqLbnbmOfRDbmuQ+WVaRlS0B1eNNPc5vcHYnkHlPu5QWepJtEs+nitmFjyDBIFshAMFgBRxnNjtiCrdwHgERbxlPFKJoBSVl+cnKPRG1yt7EPIis990FStkagdrhhk/sAIOKb3+6uxCOilOGnVLdlEmHbMjb2SWQluUfj/2cK2WbLDFMvIrfJ3aLcJYIObyUA1aKZfI+LPHf3QU4ZIfc9a2D74KXv27CRcWTjCFVTuQ9CQFVqwx9fsJX7ANDNc1dlDEaLZrwuBwXe7pmeGfHcX/sF/Pe7A9+PDRtDhWxU7tpg2TJGjyBLyH2YMvRym9wTs2XcSrmPMsm9u3LPiOceCao/GzZyBoZyz4JAo4HBsi2yZcCWrdwHgISAaqeh3GnG63ZS4HZwi+suZoqt5joZsWW0CETDva9nw0a2ICtTIQcpW8bY33D3UmzPfQBwxDdfc3pokoWMFs34XA7GuVq4wPUa93p+aa6TkcJhWjTzPqENG4OJbLRlBi1bJkvKG9vKPbPYI8sYLVqUcvcoW6aAgPm5lgnlYpO7jVyC9ZrPJnLXBnGEqvX/cMEexJRZ7JVlpude4lYXTaGIkXskmoEfXEbp6Arwzf9bPvB92bAx2LCS+3CrWSsG3XPPEnK3lXtmoJS7IvciV/eLJjOeexQZDfPJrraB78uGjcGGlVyGm/CsGHTP3bZlRgQkAgHsoYwqWvA5ocjZvbuXkVRILYKDqD2rk40cQZbaMoNWFTJLgsfa8JJ7ryV/cwpCsEeW4RSSStFKJBm5Z4KQZRSnjNqzOtnIDWSrch8shT1YPYI+t8P23DOKPVLN1V0umyiMs2UUEWcqW8Yho3YpAxu5gbiAahZ67hmfiSnbUiFtWyYjMMi9NNpIviOWi15IF6Cu8wHbKVoUJxFbudvIDcQp9yy6ZgdLYcssGbBl57lnDgJolMUAFEVayHfEFEG58JuvB+y7axEcSLRoFqkgGzZSIVttmUHLlrGVO6RB7kKIe4QQe4UQqy3Lfi2EWCuE+FgI8bgQolRfPkkI0SWEWKH/3TmIbU/SVujCC0CBI0y+iCn3CmKZLQO2U0zFYY9StZELyNKA6qDVc7dTISE95X4vcFLCsheBOVLKecBnwA2WzzZKKWv1vysy08z0EUSV+vUQxmexZcpFjNwHbKfoHqGwBzLZyAVku3IfrFTIrAmoZim5SynfAJoSlr0gpTSY7T1g3CC0rV8wyF1EguRhJXeLLTNgch+kQJANG4MBexDT8CAHlHtv+ArwrOX9ZCHER0KI14UQS1JtJIS4XAixVAixtL6+PgPNUNdwBCdRKSASwEvI/Kza8nwaOLkrUndIm9xt5ACyXrlnuvxAtnnuORhQFUL8AIgA9+uLdgETpJTzgW8D/yeEKE62rZTyLinlIinloqqqqoG0Qu0Po26MIIhHJ/cwmhTUO0cz1bHD3CIy0G7SYM3absPGYCDra8tkuE22cgcGQO5CiEuB04CLpVRXj5QyKKVs1F8vAzYC0zLQztSwTNhheOlB3BAJ4pFBAnjY6ZnEVFFnrjdw5a4uSqfU7FGqNnIAWUrug5bnnmXknkuDmIQQJwHfA86QUnZallcJoWbQEEJMAaYCmzLR0JSw1HSPxpF7AJ8jgnR5cYyeyX5iJy4icev1G/qP5RJ2rruNLIamdZ9PdLgJz4rBmkPVLvkLpJcK+QDwLjBdCFEnhPgq8EegCHgxIeXxCOBjIcQK4FHgCillU7L9ZgyW2ZgM0g7hgUgQRyRAQX4hRePn4hFRJoo9cev1G/rF6EKzR6nayF48+z148OLstWUGrZ57Cs890Ao7lmX2WD22Y3g9915ry0gpL0yy+O4U6z4GPDbQRvUJSZR7xOGBSBcgweUlVD4dgGmijo2yJmOpkE6iun/ffTo/GzaGHS1boXVH9ir3Qa/nnkCqy+6FV34GP9jVbf7lQcEwFzDL/RGqltmYWrtU6mPE4dXnOQ2AO49w+VQ0KZim++6ZsmXc2PVlbGQxtKgiuGwld7NMQIbblKq2TLAdosGhS4QYZnso96tCWmyZkD4Rh9PjU8QulXJ3ePLZSQWTHbshmrlUSKXcbXK3kaWQUZ1YstWWGSzlniILZ6irRQ6z55775G7pXs0aU8xR06qYtLpcKXcpwZWH0yHYrFUzxbEbGCC5axrGzeK2a7rbyGYkU+7DHWS0Qm9XJBLhg40NHLpfZYb2m6JHMNSTeORynntWQFfuEoGmSc5bNB6nO08p90gAXF5F7nIMk8RuQA5MbVt+KFu528hqSE2p4mwNqOpkK7Uor3y6N+P77XauQ63chzklM/fJPUmeOy6L5+7y4RSCLbKaYjooxz9A5R67MNzC9txtZDG0qCKYrPXcVVvcIsMiKZViHmqyzfZUyKyHo3sqJKZyD4Lbh9Mh2CSrAZgkdicl5Hc3NrK5oaP341n8QSeardxHKjoaYEeOT4AukwVUs+h6tZBvNJpB3z1VKuRQjyzP9sJhWQ/Rg3IP68pdt2UApjh2JS0/8N1HVnLnaxt7P57lgnQRITpMP5yNQca7d8C/PjfcrRgYtGh3C2K4J7CwwtI2LZJJck+RpWKQuh1QzRFY8tw1Q5W4fBDuAmfUJPc6WUUINzPEtqTKvTMUoTOcxo+uWcndVu4jFqEOCLUPdysGhqTKPYvEiKUXEcnkxDepPHc7oJpjsHru0RSeu0MQxclnnpkc5Pg0KbmHIhrhSBoXfhy5R2PHtDGyIKMQDWeXjdFXZHtA1UJ6MlMT30iJmfo53AFV23MfIOLKD+hfokvPcw93Kc9dqMqR63wHMFtsRQRau+0mFNXMPPkeIePJXcvlm99GamgRQGZX6mBfoWk5EVAFMjdlZU/nqg2xks7FwmFZBcsI1TjPHammwXP5cDoVuW/MOwCHkBTt/TBuF5omCUclobSUe8wbdNmpkCMX5tD4HJ5KMZktk00PK0tbZKYCqj2Ru63ccwzWPHer527AFVPudYVz6JIeKne+GrcLQ7GnR+4W5W6nQo5cGL9zNIfJ3QyoZqsto1leZojcrcSdNQFVW7n3D0k993hydzsduJ2C/PwCntUWM2b7fyFkVio2yT2Yji2TqNxtz713dLXAG7cOW0pYvyBHALnLqO65Z38qpDYUyn3YAqp24bD+IUlVyDhyz6/A43Lw4OUHc9FBE3gocjTuSDt88h9zFSOQmlZA1XLBuOzCYelhw0vwyk+h4bPhbkn6MFVeDpO7WX4g+5V75jz3aPLX1vdDrdxtz72fsARUC7w60VvJvVjlty+cWE5pnof35Qza88fDqofNVUxbpj/KPZfU6HDB+M6ioZ7XyyaMBFsm2UxH2UTumpXcB8GWyRrlbnvu/YNuy5y7sIbrT56hlrm8sc+LxpgvVWBVsG3MSbDpdWhXE3MbXntfPXenrdzTQy6q4FxscyK0JEo1mwYxDUagtycLaqiVtO25DxA6uR83c3QK5T7WfOlyqMDq5jEnqS/8kyeAvpJ7TGG47WyZ9JCLKti4MXOpzYkwbQjLOWSTcrd67pkKqPb0wNjHRqjmPrmLJDOqWJW7O8986dCzZpry94PKabD2aQCCkT7YMnFVIe0JstOCacvkEFHmYpsTkeyhmlXkbiXikRxQzWJyF0LcI4TYK4RYbVlWLoR4UQixXv9fpi8XQojbhBAbhBAfCyEWDFbjgeTTZVmVu3WxrtwjEph+Cmx5C7pa+p0K6R7uCbLbdmZX3nIq5GLOeC62ORHZrtytee6Zuo57sqCGM899GDJm0lXu9wInJSy7HnhZSjkVeFl/D3AyMFX/uxz488Cb2QNM5S5iy9zJyd0YzBTVJMw4VamF9S/GbJm0Aqrxyn3YPPdAK/yhNi7rJ2uRiyo4F9ucCCNgaQ1WZpMYiMtzH4oRqkNcFVLrwf8fAqRF7lLKN4CmhMVnAvfpr+8DzrIs/4dUeA8oFUKMYbBgjFC1/pCGcvcUxq1qDGaKahJqFkHBKFj3TJznLnv7ESxqYFg996BfzQfZnsFJDgYLuUiUaXju/kCYp1buHKIG9QNJlXsW2YjW2jIZy3PvYRDTUAc44x40Q/9QHYjnPlpKuUt/vRsYrb+uAbZb1qvTl8VBCHG5EGKpEGJpfX19/1th5Llbn8aGms8rj1vVadgymlQPheknwfqXCAcD5jrh3gYlxdVzjw5fyV+DdKLB4Tl+X5CMZLIdaWTLPLtqN1c/8BF72gIp1xlWZL3nHrvXhla5D/FkHcnaMgTISEBVSmsptrS3uUtKuUhKuaiqqqr/BzeI3Prl5ZWq/wd+JW5Vw3M3g6DTT4WQn6Ld75rr9GrNJFaFHC7lbpBPJAdyx3NRuZvEmFpRBiJqnbRiNcOBZB5zNpG7pV1iUDz3RHLXf8vhUO7DYIcNpJ77HiHEGCnlLt12MfyBHcB4y3rj9GWDA1O5W768gkq4YQd4CuJWNZR72CDkKUeCO5+KXW+gQgX6jeolNRLIfdg891waGJSLqZBpfL9GLy9r02GTBYWzNM9dykzZMj2Mxh2ugGqytgwBBqLcnwQu0V9fAvzHsvxLetbMwUCrxb7JPIxsmcQgibcQhIhbJISgyOuitVO/Yd15MGomha3rzXV6VWGJE2QPV22ZXLJlcnFAUBpWUkTv5WXtbFzJ6uNkk3LvyR/PxD6HO6CaC567EOIB4F1guhCiTgjxVeAW4HghxHrgOP09wH+BTcAG4K/AVRlvdVzjjIBqel/e2NI8drZaPNLK6RS1bzTfhnu1ZeIHMQ1bPXeDdHLClslF5d57mw3F3m/l3r538AKc1gdOtqZCDvYI1awKqA79956WLSOlvDDFR8cmWVcC3xhIo/qEZLZMDxhT6mNnSxcA/121i4PyJ1ERrKeITvzkmwOaUsKaCimGcZo9k3xygdxz2XPvSbnLuP99QmcT/G42fP4fMP3k/rSwZ1gILBIO6ze6yC5yj8tzH8LaMsMRUB2G3l3uj1B1JAmo9oAxJXnsag3Q2hnmqvuX86tlavn+QoUFerVl4pR7ZPg895yyZUZmtoxRNK5f10BXs3ow+3f3p3W9w0JyD32wSS0STjbXZ9G8sJZ7NmMB1R5tmWEMqOaY554dMGyZNC+OmlIfTR0hXlm3B4B1UVV7Zn+HTu692TL6jxSULpxow+e529kyg4s06rkPKKBq9LgGy/+1EFhHp7IhIzhp6ciitM0ET7rXMSb92Gf8Z8MZUM1Szz2rkSzPvQeMKVG1Zh78QKXii7KJRISnz8o9iBv3cOa5G4rStmUGB2m0ORZQHQC5D9Z3YiEwh56JogknIptsGUtbMjbaW+tBLQ9rQNVW7n1HHwOqY0rV6NX3N6sBt01dURp9E9hfqJGGvQdU1XGCuFW2zLDZMjmUCpmTg5iM8rAp2qxFyQuo7N9IOmUrEmH8fkOg3B36MaI4gSwi94RSHvL1X8LGV3vYIA305HPvYwHV3Cf3PgZUx5bEqkTWlObR2B5ir3diP5S7x85zTxcjUbl/8gTXrDmPQjoHaMsMlnKPXcemcseRtcrdgYbr/T8NvFZSWqmQ+8YgphFA7kaee3pfXnVJrKjYRQdNoD0YYYdrAuNFPV5CvWfL6BdPULqHmdyNVMgcCqjmErnLXrrw7XtxyxBFdA3Qlhl85S7019Gss2XiBwQSCQ78YdeTz20GVPeN8gMDGaGaHTDLD6RH7j63k/932iwWTy7nk51tAHwaGcNJQrKf2JlG+QG9yBhuXMK2ZdJCLg5i6q1npD+o+l322fguBk25d/fcozgRqOJ4ImGA37DA6rkLDRENDlwA9JQKaY9QzTH00ZYB+Mrhk5lTU0JFoQeAFQFV82x/sbMPtozLtmXSRS7YMkvvgccui703y+Wm8tx1cifSv6C6mco6SN+JdSS1xZZxIHsvjjdU0DSkXqo7H70HOtDrOZtK/trkPkA4+hZQtaKyUBWR+bCtjCiC/R11aZcfMDz3bqpt92r46F99bkufYY9QzSye/lbcpOmx3kYKItB7Th76qdwHOxUyiXKP4MSBzJ5J3aWG5nADUICeojnQaySrSv5argvbc+8H+pjnbkVlkSL3Ts3FLjGaKWJ32uUHlOeudVdty++DZ7/f57b0GaYaziHPPRdsmaA+yMfMc0/x8IxT7v0h9+FS7hrhSJYodxk1yT1PGMo9k577MAdUh7kaZ+6Tex/z3K2oKPCYr/c6q6kRDexo6aIt0MMFpv9gbRQwWjQhEwOaoU4Idw7+pAi56Llns3I3YIwY7a3N0Ri592sgW3SwPXdrDrkeUNWVezirlfsAr+ee8tyNB96wBFRt5d53JKvnniZ8bidFPvVwaHJXM07Uc9cbm/jZ05+m3kgn90eiR1Ih/CxoeSH+83CnastgE1lO2TK5RO56AdPeehv6OXlEf5X7IA9iSsxEwbBltN57p0MFLYomFLnnZ8yWiZ3b2+sTZinrzWrLNGzPfYDoR0DVimmjiwBo9oyhSrRypGMlkT2fpN5Av2le1+axRpvIkuZ/x38e7tL/d/arPWkjlwKquTCIKa9M/ffv1tWfTtipUhUtyr1fSngIPXeXqdwdCGQW2TIW5S4ypNwtD7Vtjf74z+w89xxDqnruaWLO2GIAmj3VANzn+SW/qf966g20CJpwAoLn5UGMC25UFf4MhDvU/0hAkYRB9pmG6dnmALnnQkDVJPdd8V3olKmQarmnv577YPdmEub6hVhANXtsGYvnbmTLDFQApPK5rZPFDcsI1SydIDur0cfyA4mYU1MCwNpAeS9r6tCiSP2YK8VMtazuw9jnVuW+9G64bf7g/LBm4bBcCKgOcXe4P3Dq8Rf/rvh2prRlBuq5D6VyN7JlHDizyZaRkqhQPe9YKmQGA6paCuU8DMo9GB56EZb75D5AW2buOEXu7zbmxy0PRlLsT4sg9QtynXMqEVywLTYHa4zcA9C0SZHFYBCwdWBQNs1onwy5YCEZv5F/V/y1FI1AVwvULYtfX7dr+p8tM3RVIU3PXTrVwLusyXO3eO6DYMsgtVilyZ7KEgwWLMd55uPBm2k0FXKf3KtmqP81C/u1+f5VhQC0OssJSnWhaVLQ2Jqi7rXUTOWuufLY4pkKW63krnvt4S4ItceWdTbBuuf61caksCqcbCZNyI2Aqknuu+MJNxpSPbC/n0yy2Y08/R2hGh3k78TSVrdQxNaJjzyCvY/CHipIDU04iEpBQcYGMcV+Cwcy9uCN640NVUA11pa2Tlu59x0TDoJrPoKFl/Zrc5fTwZ1fWMDj31jCUjmdelmMQ0ha925PvoEW1T138LgcfOydD3UfxFLoDOUe6YrlTIc64KN/wgMXQNCfZKf9gPUCzXZrJhfy3CO6cmzbmdC1D+sTawTjiccSUO3fCNVBLhyWRLl3kEcewexR7jKKRBDBaVHuAyTeVDOlDYstEzuONlg1hHpAv8ldCDFdCLHC8tcmhLhWCHGzEGKHZfkpmWxwUpRP6TYZdl9w0pwxTK8u4pCb36LlxNsBePrNpbyydk/3lbUIkhi5v+k7WpHB6sfU5yGrcteDq6EOPegqY4Q/UFjIPRLOEXLPBeUe7kxQ7hFlsUHsAQDmOu6BjlAdgnruBrm348MrItlzvUgNDQcajszluVtnd7LGF+JsmaH33KO5lC0jpVwnpayVUtYCC4FO4HH9498Zn0kp/5uBdg4JHA5B0aiJAGzbsp6v3Lu0+0rSotydDrY7xsHY+fDxQ+rzpLZMBwRVkTKT8AcKCyn84qmVmdnnYCEXbBljpG8klOC5h1QvDOJ7SHHKfQDZMkPoubdLVRE1GszQNThQaFEkDjrwUYx+32TIczdLLRi9lFTB1cGEhdy1VDG8QUSmbJljgY1Syq0Z2t+woXT0JACqRVPyFbSI6bl7XQ6CEY3InM/DrpWqrozRzQ53xSyYUCcEDHLPvHJ/flUKCylbkO1VIaOR+KCv5butb22PKXdrqQfDc+/vhC3Dodx1cpfZQu665+6XeTiEMa4gM9kyEZwqM0izlftAcQHwgOX9N4UQHwsh7hFClCXbQAhxuRBiqRBiaX19fYaaMXD4isrwyzwOcGxieokGT10LL94UW0HT4jz3VTtaOea5cjVSdvl9sfUiFlsm3Gkh+gzdWBYC8pKlpGkgjflIhxUGaTs96rXl5m9s64jZMXHKPVPZMkOR567a6td0cg91wK6PYfk/B+fY6UJqSBz4sWSqZSjPPYwrQblHuq0z6IhT7hHY8DI0D53+HTC5CyE8wBnAI/qiPwP7AbXALuA3ybaTUt4lpVwkpVxUVVU10GZkFFvlaE5zvsfPQ7fAiv+DtU/HPtQiaLrn7tB9/m2hIphylFrXgNWWCSXYMhtfgd/OGhjRW4jSQ4T2YBbnkGe7526QtrdI3ZCWkg4uomjhJLaMmS0T7l/euJktM1h57rE2GcrdLy3kvvwf8PyNg3PsdKF77m3SQu7REM9+vHNA+wSISkd8qYVhznOPaho8+hV4789Dc2wyo9xPBpZLKfcASCn3SCmjUkoN+CuwOAPHGFIUXPIwbxedxEK5Wim5ps2xG97iuX9c12pus8U9Jd5yCScod8OWCXfAjmXQtiOWYdMfWJSIm4g58Ug37FwBHQ39P04mkO22jKHMvaoUhRE3ieLETQQZGgTPPZPKfd1zsOWt+GXWqpBCkUy7VFVQCXWqnqU1QDwc0KJoiHjlDryxbgD3hU6oYWM0bjRZnvswKHctoq6rUIay5dJAJsj9QiyWjBBijOWzs4HVGTjGkGLyftPZNOULsQUyCk0b1WstgtS/tq5w7CJ5fnOCAgt3WpR7Z5xyj/r1LJyBpEVqVuUeZu3uFOT+r8/BW7/r/3EygWwPqFqVO5jprGGHB5ewKPeknnsWZMu8+r/w9h/il2ndbZlWTZ8/ONyhzjkaGt4BcLrn3iYL4hcPJLXXQu5OtFjt+mFR7rHvVotG1PcdHroH6oDIXQhRABwPWKtn/UoIsUoI8TFwNPCtgRxjuNBVPpP1Wg1akf6sql+n/mtRorpyv/9rBzFPH+Ha7k4ILXQ2xl6HOywB1Q42bNwAwO50Yw2apmYKstapsXTnH/X+hNHbUyQlBVrUCMvhRM6Qe4n+Xn3PEeFRdVlMW8ZyY1o99/7kjWcyWyYS7K7Ck+W567aMCFniCMM5AE4ayj0vbnE0MoDrRIuNxhVoMc99OMrvalFzNLvTEAaDVWsqCQZE7lLKDillhZSy1bLsi1LKuVLKeVLKM6SUuwbezKFHUZ6Hi0M30nCePht7w2fw3p2w9mm8EaW4D9u/kq8ePhmADR3xFygdFuKO89zboV2VIq1vSNMu2b1SzRS03lJeOIEU5m+9p/t2ET3zI1MZOv2FqZ6ytFRCN1tG3YAh4VW2jJnnHiNCadaWGWC2TEbIPdB9IFuccjcGMemTw4c7Y+sP5wA43XP3y3hbZmDKPT6gOtyeu9QLG7o04xrKEXIfySj0uthLGS3esVAyAfashpdU1kxD/hScDhVMNerBbwvEX6C0W8i9fS9GRTot2EG5bAYg1NmSXmO61PpxNo4WJuL0mW/b3KO6b2fm3A9y+eHeMByZCn1BClsmJNRUiiKSTLnHJshOa4SqlCqIaRwrkzMxJVXu3QOqBrk7IhZyT6XcdyyHBy4c3N6WprJl2kQCuQ/kmAmpkJGk5QeGktxVSRNnVP99ckW5j2QYpO0PRFSJg0+eVDfQOX/j31NvwSkMclc/XqMsjt+BVblbAqfBzjZKoiqHPtTRSlowbBVrdo0WJeKI9RbaHSWKQF7+iQqiQuxCCvWB3N/6PTz/g/TXTweJtVqyDSkCqkG8eAgjklkY0T567rtWwpNXq3Q4674yEVDtRbk7TVtGXS8Ow3OH1Mp9y5uw7r8DD8aHepiVTGpEcdAlEjz3gVwjhi2DU9WuH+YRqkbyhcsm9+xBjNzDsOQ7aqE7H2acSkh4zXm5zZmciJF71FMMnZabwh9zprS23Xj0LlqooyW9xgT0h4BVuUfDhC3K3RnVfdQ3fwOfPqkIvk1PKeuLLfPSTfDuH9NfPx1oEXDpD6JszJgxyCRBufsdRXhFBGdY//4s6lj2NVvGsOWM39BU7oPvuRu2TCcqW8ZpzZRJlTFjtHMgNoJ/N/x8DLz/l+Sf67VluhyFcYujA5ldLCGgambLDJsto/jBrfXyfQ8CXEN2pByDocjbgxEYNVMRvMMJnnwiUYlLZ3djvRBuc9sudwmFHZZRoxbl7mjeZL6OdKbIcElEoEX9j1PuYcIW5e4Nt8eCtsF2uPdUmHyket8fWybcBe683tfrDVIqonH7FFEMQwGlXmHccD79Aa1/X21Ckb0wiDIShD2fwLK/mw+EtGvLmHWG9AdFpuZQlbJX5W6M/ozioFN607NljBpIA8nu0GNLLL8PDr4iSduVcu9wFJjzaPTYpnRg2jLGICYtbjkwhFUhY8rdrVlqFw0RbHJPgUKvxZYBNh/wbaSUTAE0KdEtd1O5W1EXyGOG8cZbAh2xuRw9rVvM19FAuuSuK/c4co8QcsSUuzfaHlNbXU2KRFq36dv144Jq2gyjZ/V9u0QYN5UrD2geXFtm02tQMh4q9uvbdqbnbpC7UqttFHZf77Nn4YO7zC6vh3B6yt065gEylwpp7KcH5W4uQtCJF1ecck9hy2RCuRvF/AIp7Ec9z71LKHLXEDiQA/tOLJ67Q6RQ7kNYz93IlnFLg9xzJBVyJMMg7fZAhGAkytG3vsaJv3+DHz6xinvf2WIGVAs9rm4FKfeELQGiwligs0EW44zECFqkm+dukrvFXolGaHVXcW30Gpa6F+KLtkNQX8/oKRhB3f5kyxh5/Yl4+zb4y5Hp78dQSW79QTSYtsw/zoTb+1HX3/Tc45V7C0Xx60WD3ap6ukU0vRGq1jEPYPke5MBsApOkEx6aSfap6crdGU1DuRuDbQZCRsa2qchdRtEM5Q506QFfkYFUSGOEaizPfTgCqhKtG7nbnvuwo0AnbX8gzAPvKwUcjkpW6aNSDXJ3OASFnnj17jdGAgIUjjZf7pWxXPjtWlXMy+0NekD140072NOm3zBamLB08qprCQ2uavI0i3I3yN0I6vanK9i4Ifny+nWw99P092PcVIbnPuDCUBIe+xpsfDV+uUlCCSp66zsqmNkTUqRCtsgkyj3hQZn2HKqmctf/x022MoDvJJJKuXd/4EjUhB2uaDrK3YgzDICMjG1TiQs9FbJTqO+5gwzEZXQrJIojvraM0ZNxeoYwoBo1pxH0GLaMnQo5/DBIuy0Q4e/vbAEg3+OkoV3dTNYEAEPlhz1K+QXxxD4sqDRf7tbJvdlZwU4qyNM606sJoyuf5uYm3t2oD47SIoSlE5/bQdBZSL5m8dzb9RGwZsGuUHoEYknp+/jj5cnXCXcoBZtu0CtRuQ+U3IN+WPVIfM4/QHuKIevPfh9e+VnP+9TPpTGifre6veo7bk5G7onK3eq5hzrUWIhkqZGm556ktO1AyMwgaRmNj2fo6jQknbFFOOjCizvSZVHuvdgyA1HuveWraxpR6SCgK3dzBO2APPcoIJCI+PliDbXu9A5pQNXw3L3mBOCRIRvMZ5N7Dyj0uXhvUyNbGzuZXFlAZyjKbl05N3bELkAjqLrzotc4I/hTc3moeAIteiW+bY5x1MtSAOrcE/HLPApFJw3+NAZs6AHVfBGgIxQrOBWWDrwuJyF3kcplNkg9mMTLT6dImVXhp1LuBjmla/UYN5JheQy0KmaXXoq5fW/8cqOkQyJCHaltAQM6Qf7rI7XvVVvUg6IpqXKPt9LismXe/A08931Y82+6wTpxC2RQuVuuH6t6twzmMRcBndKLW+tKbeeY7e2eIdRnWC2IZOmQUkNDIJ1O/KKQJt0GE9rAAqqGchfI2IPXVO7uIQ2oGsrdJy2/0xBZMza594Ain4u1u/24HIKLFk8ASNoFN5R7efUE1jqn4kCphc2H/ILN9YoMXmMhAT2jZqtzIu3kUUiXGbA10bAe/lALLZZsG52cCgjSGTSmrIsQkg58bgchl24ntPZQ1z3cyeodrexq7eHCshB2cTQFIRrklOwBkgwGuRtlHDr2dl+nqwX+cVb8OaeCUdahPYHMjXRTb8J4A2td/VTQCXJLu1JZebrKatQSyD2Z525V7gZJtyQp65rMlnHq9t1AyMZKvnFVK3XlbsniUgFVnwq+m726XmyZgRCRtT3JxICMEsWBUwh+VfUz7oicCcAvIremTp/sDZpKr9S6KXf9v9MzpAFVo4KsT1ge4EOUDmmTew8444CxFHicnDi7mv1HFaZcr8jnwukQFHpdFHld/Dx8EReFbmRX+WKqWlXdtKe75lEhFMlsFhPpEvkUii6VR2/F5jegeTNsfz+2zCT3rphy18I6uTuJuA1yr0t9MqFOrrp/OX94aX3qdfQbOoCXAplCYRvklO50gQZxFevknqi4AfasgU2vQt2Hve+vM5Vy120ZX0lCezvTIPcAOL3s9Kub3i2VcmzW8tCkJVqezHO3jlDNL49voxXJbBmPHngfELmnp9w1BOjZMgXWB3cq5W48vAdCRFZ/OVnPSlfuDoegvmguu2QFAD5CscFefYWUSOFE6p57OKGeu3S61Wjz2xcNfukFqZl1qAzBAAxZOqRN7j3gm8dMZeVNJ3D7hfOpLPSmXK/I56bY50IIQaHPRT1lvKPNoSMY5Xfii3yk7c8yOY1xQgU4t1KN5imiiC7aAmHoaqHt5d/y7X+9RXi3Hqxs0ElYSjOgmi8CdIZitdFDmhOfy0lE9/p7Jvd2mjtDtHT2YAHoxFUvKiiiI9ZL+eh+5V1DjJzSzfQxiCuZcjf2ZeTxB9t690NTKXfDc0/MzQ939V5mNRJEurxs96tj+/QbMRB10G4tapXEc/cQtUw4rT8Iko3qNKdctGTLuPWRmQOyZQLJX5vK3bBlVNs6pJeCaFvybQxI2b29/YHVr08WE9FUtoxTCIp8LsLE4gO07Yi9XvkgfPZC9+2TQS9GpmwZzZLnrte0j+iU17he3S87lsPdJ2ZuEp24tmhE9e/fh+UhOkTpkDa59wKX04HDIags8qRc58zasWYBMSM/HqDeH+Ax/yzODv2EKE4ejB4NwDomID1F+ESY2W9dDa//iuI3f8z5n32HQN0KtXHDZ+p/uAu0MBJBAUE6jACsFiUoHXjdDjRP78pdhjroCkWV8te0FEE/dUPvphKfCNPRqV/wnz4JK/WqzomDcXqDQe6eAmWZGOmZez+FX4yDvWtj5RUaN8DPx8K291LvzyD3QEu88jKUexzBabqV4u+5YFk0iHR6aQ+r2yFPvxGDUUGbtdZ4JBBHAiHp1GvL6Ps2LAxr6QlzZcv3pkWVNWA8iPqi3D99Wk3naG2TeR4WAjFGauoBVU0n9zYKzFozAMFgEtslEoy1aUABVcu2yeYukBpRKXA6BMV5bsLSknVmvZZf/xV8cFd6x9QfGEZANVZbRp1zUMZsKtp2wAs/hO3vwbZ30zypPkAfpAWQJ2zlnrWoKEit3I+dOZpvHjMViCf3VTvifekHo8dw/pjnaIrkkedTD4vxu1+E9+6gy1POQY61FO3RrYnG9UgpeekjVWrY764gXwTpCsZqkoQ0ZctoRqlaq9pJQDjYzu+dv+eo5kfhH2eoizoROgHt0rN6Ott0e6Ftp7KGwl0WWyZNz93wNx0uKKiKKffGDUpNNW+JKfddHytCMMorJ4PV8rBaM4bnbvWIDVtAi/RsL0SCRB0eU+Uayr0rKvDr9VjwFCrytPQCuvTaMzFy17+bZA9Zqy1jkLBhy/RFuT90Mdx5WFzbY6+7K3fDlpEGuSdUYPzrq0nSWq29sgGlQlraYzzwopFY70cnP4ep3C3kHmiJrdfZkL6YkBpSOBBOY7KOeOUeIeEBUjxWvW7Z1rdzS6stkohIotxtzz274HE5KMlz43KIHtezjlhdWdfS7XN/IEIwotFUMpuwdFKfrx4Kb477OnVST5t0eqFhA8u3NvLLJz4AoNmppiKMBGLD1wM6ucvEIGIShDr8HOdYzuzACtj9Mez8qPtK+k29Q1PecZdfr0ZpEKd/t8WW6eVmiwTVMQwF6HCqAV2GcjfUetAfe23cYD09OKx18q0Wj6EMrUrTSvQ92UiBVoLOfDP4mCfUjRjFQRvKOol6imloaYs77058uInEJmE2vpuWbd17CtYRqjqZS7ci2s6Vj8fSWPuCtl3xdoeV6PW6LVHd6jDIvTOhjktnVxdaYpKA1cYa0CCmLhAOQKiHcjQMv5sFv6hRVovU0KTA4VDWZpwtA0qsRMNKWKQb49EHRjkcTpzCUs9dM2rOWMl9h+pRgiorkWlo0Zhyj7Nl7GyZrENloYeKQg8f/eh4Prjx2KTrWJX7hr3tWJ8FQqhaNcFIlJ3lB7GA/+PhSTfDzDN4L/8onojqimy/oyHSRf5HdzNTqMyLba5JAMhgu1mvJRh14HM5kHnlRGTyn9K4mCPN2/GJMFXRPepm6UFdbo8qcg/49RvSUF1tO2LZFf7d0JhiFCvAR/+Eu46CpX9X7xOVu1nGuDWm3I029ZS6aCV3I0gnpbpRIb7Lmy65t9bR5h6FhgMNhxn8iuIwlXuTls+OPXvjctI7pVcNYopo8ceLdMW3E0zlGepqJxRS+2+Lqt5b/tu3KLLrDYnBzwcvgme+Y/k8XrlrwoEm1HVh2DIBZzy5ewjHzSgGxBHphxt29G8aQVAPG3cB5JWp76OrORYraVhvkp9TCIoTlTuo68H4HtOdnk63ehxOJz5CuIJ6Ty9Jaiit22PCYu8gkLvUzJ6CIRhUI2xyzzqMLvYxuthHWYGHUcW+pOsU+ly4nYLyAo+5TZFO+JWFXp3cNbwuJ8V5HjYxHs7/J7uDbv4ROYFPR58Oh14NwMyVP+dH7n8RdhWw0jkbAC3YbqrhgJ4t4/Z4WSfHAyBFvPppc+iWjZ63PlHqBOrf2T14qRPQLqnIPdzREu+VWsn8tZ/DX49J7WUblsn7+oTADpeu3PXlZhDVotwN4gy0wZa3k2dydDZB6UT1+sEL4YO/qp5FyA+F1fpgHn0/ceTegzJu20G9cxQOAZrTY6osq3LvEAWUE08wXXqVRWn605ag3J6E2SX1B6cMdfD2OvUg6tAscRx/GpNCW62JSEgRpTWtr5tydyITlHvQlUjukVgGlgHLg3Db3qbYqOi+ItIFLi/kV6jxCdYHbKgjLltGKfcEcm/bYSH3NAOeWpQIDpwOJ2NEE9cuP0lfrs7RmhpK246YyNizJvMTyUiNSGJvBGxbJhvxw1Nn8b9nzelxnXMXjueGk2dS4FU/ak1pHmU60VcX+2jrChOKaHhdDop8LjMVsqkjxF7KeHziD/iQWcjrNtKSN4Eq0cqu0oU0RHTvN9QRI/eowOd24HU7WaHtrz72Vca1xyhF7GxWxGwG07RI94wTXbHt0T33cEdzXLlimjbFrx9oid0ciUi0GYQTCkbFAqEGoQfaYkRvYM8auPcUWP1Y9/12NkLVjNj7tc9A/Vr1emyt+m+QulXFp1Lu4S7oqGenLGdUkQ/pcOPVc5KjOE3l3kYB5SL+nMzJL4yHUqhTtc1TBB8/HH8cnZy8IkJHu2pLu2YhmvYkQdhEWB9QbTu6+9BJlLtMUO4hV7yF5yFMRzD5Qx6UVxwIR2H9i/CzscnTPFMhElRB4/wK9btZ2x/yqzx3KZIqd4lQvTEj8yhdWybQSgf5OJ0WUpWx+j1ByzE2bViL1qlfv4GW7veDlCoO1F9INQI3Lp0WciegKoTYos+ZukIIsVRfVi6EeFEIsV7/X9bbfnIBs8YWM29caY/r1I4v5SuHT6ZArzcztjSPsnx1E48u9prRe6/bQbHPrVIhgeYO9f+51bs57853WVrvYHn5yQBsK15IY0jt4472b7H+9rMBlarnczvxuhyskKoSokNXj0adDmMgjqclgZghZmVsfhM2vQ6hdqTTR5NU2TfRzpYEck9iwyTLgoDutoSh3EHZPHHKPeEBUa8H+ZINBupqgqJqOOVWlX0T7oJ6PbNoTK36b5J7GraMXvN+e6SCUcVepDOmpqM42CZH0SRK8WseCqwZD0CXXkNIGOQe7oT8SphzNqx5IkZImgbhDiJu9VtIncgbI5beXyKxJIPlHHZvX99dza74P1itj47V67YYedZSJxgzbVaHh0gsAyvhOCGHDx9hAmENnrxG9Ux6suISEe4Cl0/l/3cmV+5RXbkX57nRLHSk5VdBW11sXoR0y0V3tdBKIS6nhdrCnaYtYy3HUCUb0Tob1TwNwMvL1iCt6n3bu/CXJSpdsj/Qz894sBoP2lxLhTxaSlkrpVykv78eeFlKORV4WX+/TyHfoyv3sjxK8xVhjCmx1F93OSnyuWjrUhdsU6eyArY1qaf6qrpWXss/mRejC/m45GjqwzHFMbVNpW1FcOJzqz9DubsjilC8ZTWA8nWluwBvVxLyMEa0PnChyqD58G9EPQWmFSEDrSpoB8o7bUzygLCSvxWdjeArjb13OGNF1Py7TUIPdbaye8/u7tsm27eU0NnIli4fe2d+EWaerh4ADevU4KVSNYqYQKuyZqyZHqmUn/4dbAyVUlXoRTriyf2+6Ilcknc77dHupZ3NyS+khdzdeTDjdEWEu3XVp7cj5FWDdLxt6nvcGC6P7SzZyN1EWMjxtoef655C+dlzaK//is5QxJISGK/cw8aANx1ewrGxEwnHaXeVK+UeicZso3Ca9gionoRJ7o2x9guH6rlJjRBuM8/dirCvHK2jCTosIiGhp7Jhr5/VOxLiM13NNMtCqqKWnlDQbyp3qQdWm2UhRaILl38HlKk05rue/4itjRZVbUx2k9hjTRe6/28EtSPu+Kqjg43BsmXOBO7TX98HnDVIx8laGDdMjUW5T6yIpaF5XQ6K89z4g2GklDR3xPvL63b72RYq4LLwd9hNBeuCFeyQFXwzdDUrtSmAumG9Lgdel4MNcizN08/n+Zk/B8BRolK8uvAqFZQMRupkJGZjSOGkE68K0Aba1E3t9NBcOIVwQ5J6Mz0p91EzY+8dLihX7aZpk2nLtDY34gylCKC2JZB7oBW0CPevaue+d7Yo792/C3avgsrpsbzxvx0HL/woPc9d772sC5RQVeRVw9N1RHHgdnupjxTQHnFYliuibJXqIejTLGmOnvxYD8WwMHSFHfAoMi/0bwFgdWdprB3JRu4mwkLuU0XyMQ1a/Xq+8+BSlTUiHGYMxiB3LVG5i3B35a4HtFudZfhEiK7dG7p9lhYiAVUwzrRl9PYXjTGJs50Clefuc8dturoRtu/aFT+jWQK5H/fbNzjt9rfi1XZXM41aPmNDFkIO+s3YhDFR9UrNUvO/XJF7mfAT2mLJdzfONZWA6Q1SEpWCVl0sGYUF1+9Mw4LLADJB7hJ4QQixTAhxub5stJTS+EZ2A6MTNxJCXC6EWCqEWFpfPzQnO5Ro61JqrqY0ptzHl8eTu6Hc/cHus/ms3eM3CX9vW5BmWcTJ4s88rR3CI1FVT71GNFDodeF1KYW26dBf8olP1TN36MP9u6SHtkknAJjeXySvSvnCrTsUyWoRmKYCT+7OvYDATz6OoJ5VU1TN1lBJbDYZK1Iq9yYaXJaf3eFUN5FwqEwJ3ZaJdLZQQgo1mLhvPWtnr1bCzpZATKnXfQhVFnIPtkLdB6ltGS0aC57pGTprOwoVubviyb3I56IrHKUtHOvON0oVpN6hp65WSp3Ew52qh2OUITCKnOmk1KmTe0nnFgA+6bCUSuioTz6wzIo0yN1FBNm4UVfuTtMKMAKqRUXFpjXhl3nKc08MqLbtAG8xraIEHyG2LHsu9llfyD2slHu7o0Tl9hu/Z9EYU1j4RYGqwJqg3Ju1AnX9Wey9vQ0Wot+5gvlCjeLesDdG+rKrmaZoPvkRSzuDbWYvx5ju7iO9pwtA2SQAznO+zrSnPxeznoxzTRQZ6UJX7sb8ylGHl5B0sXlXYy8bZgaZIPfDpZQLgJOBbwghjrB+KNVjtVsYWkp5l5RykZRyUVVVCmWZw2gxyL0sj1HFXpwOEa/c3U6KfW78gbBJ4tZJPz7b7TfLCxvFvgxb58Ho0dwWOYu/R05i6ugifG51swYjURpC+k2SX4kmXHThZdc45d0b062F80dB+SQ1Ms/ILT/gQgCiLtXGNpmPM9SmaqFXz2MX8YFaE6m84q4mtnRZhu47XCpzonSCytzRlburqx6PiJplX+OQgtwbKWF3q4XcAaYcFV96oGFD6oDqY1+FPxwAdUuhdTvRglEEpDtOuUsEUif31q4wAcvoyQad3HcKdd1WSD1mYNgyeQk1ZnTl3uFWy8sD24jkVZq2DqDI581bey4hoZNNoyxinEg9cfXowGYz31tLUO5jSvNM281PHh4isWJ0Blp3QHENAenGR4jSdovP3ifl3kVQePjxK3rvrlmPoRRVmw88P4U4BbidDvLcTj52zOA34XNppYC8aHtcKYe7X7FkID3zHf7XfQ8Ar67Tez3hACLSRZNWwOPz7+Ft18FqucWWcesVJ1fJybF96cp9pkNvX2JKbjqZTMkgNaISmkWpap5w04WHUGAQSh0kwYDJXUq5Q/+/F3gcWAzsEUKMAdD/p9HnHFkwbJmxpXlcvHgi//zqYmpKY+TjczkoznOhSahrVuQ91uLJd4Wj7GhRy3e2KrVRXaICcBFc/DbyefaICmaOKcLrUj9jMKLRHBJscEyG6rk0zv0aL2iL2J43ky5XCbdFzqJN5hHwVsKBl6lBRh/o1fdKJ8C31/LGCc8C0EY+JcGdiohrFrBBG9PtHDV3QTwB1y2Fxy5TN1Oone0BK7nryrdi/zjlXhJSN/5eZ7fOnSJzazqkQe6yWKXnlU2MfTbtpNiEIKDUu1llUsTIvWEDrHlcPdSe+h9o3kKwYBwAVYVehE7uRiByrP6bBS0pdPU6uXf41HcymiY1EMiwZTwF6iFhKHf9QdbmUg/IUaHtdHpHdU+Te/VnsPyf3b8H85zUOdTJKsY6Uqu/mtAW0DQiUuBwWguHqdRcw07qFAV4CXefU6CtDkrG0SHd+ESI0cGtrNEmql6AkeWUDiJBgnjMAD3NW/TxDjGh0Ea+OfHNVw6fxH8PvI/bo+fQJvPJ1/xKueu9j2BHq+oNhDqQe1YzUewBJG98pj8A9GuqlUI6Ri3gwfyL1PKOBpOwvVLdS03SYk+VTgJgrEgoSjdg5R4liqDVUap2J134ye/fgLV+YEDkLoQoEELNIiyEKABOAFYDTwKX6KtdAvxnIMfJRdxz6SJOnlNNoddFSb6bQ/erjBvg5HU7zTrwmxvUk9xQ9osnlcftq16v+T6uLL4o1pTKAvI9LrwuXbmHo7R1Rfh+1Z+g9kJCx9zMu9psmjvD/H7h8/w28nne1ubQWLGQqz+dRYtvHHz0L7Wz0olQPIZWt1KjXY4C9gusUZ/VLGJNqLrbOe4pmMH2bZtiFsfqf8Oqh1XuObCpw6JM9Vng2womwZ5Vpgfq0Sswbpd6783ieauDrIrZFfpN1yBL2N0W4Gv/jqlczV2ANCYEMWAENAsqY+T+4V/B4Ybai1SZg/q1qk1AVZEXodsyRubG/Akq0esDbQbbtCqWaVPZq9flFwWVhB0+RotmwtGIil24C1QXLK88lgWk9272etVxnGi0uFL0VlNNbwgQ9KPhYI8sw0PqzJFJ2haQUSLSgdsVXzisutinCAaIuIvwiAidQcvArFCESHMdlNTQqSnlPi6yjc/kOMKuovSUe1ezuibCXQSlm2ad3PduW6cyhjyxXHs/BTj0Lut1J87g+FkqXtEqC8iXXeDfjSxWyQGE2uHhL8FfjkBEAhSKAOX42d7cyV/f2MSvn1A1iVpkIYU+F0GX3ht84kpTxPh0cveTR9RIUSyooB1Lz7Ejkdz1jKqmPgZCpUZUE7Q5S9XuNBfNspD8SItKL33gQnjj133bZx8wUOU+GnhLCLES+AB4Rkr5HHALcLwQYj1wnP5+n8IxM0bz5y/Ez+cpLL6L1+Vgql5G+P73tyEEzB2nFOHhUyvJc3cf/GD17AFmjVXr+9wx5d7aFabYqC+ve/3X/3sVf3ldBZiuDH+LN0Z/iafX7OV519GxneWXU9fcyWd7FAk2uWNkLsfWsjIQmwv2GseN/CFyDhs68xjfsQbt9/PQWnbERvm9/XsANnR4YxNe6OS+OhAjNZkfU3CfhvT9l+iDsVw6Uf/1GFh+r3qtd9GbKKIzFOWldY3cVPAjuGYFJ/z+DX76/Ob4L8zIUS6oomH3Nl5Zu0dNuzd5CUw6XA2a6qinwavsnaoiL8KtHkhGhsP8CaUAvKPN4XTnn/hc6MdmpcjSwnw6vKOoFs1Eg/qNb1hDeWUxW0YPOm8onM8e/cGwl3IzBe81sTjW5p4yM4J+Qs4CWhMn7rZgqTaNQ1mF1tVKWApcLiUgDOVeXeKjTeYTkQ6EJ5+DHZ/yhQ/OMB9+D7y9Dlegka68atqjbiqEn2oaWK+NI2CQu5SwY1nyBqx/CX45CTa8BJEgATw065NwVIZ30RTxxpF7m4wpd1D2DGAGIWnaRKBEBeKdIT9sfTtuIpl5Bc20doV5Z2MD67dsM7ct8LgIO42qm7Hen1E3qE3m04ge8/AUxY4HMavRElB9de1ulvzqVV5YY0kg6K2CqVS9J8OOi0TCNMsiyoWfHU3tauxA3dKe9zEADIjcpZSbpJQH6H+zpZQ/05c3SimPlVJOlVIeJ6URcbJhwOtyUDu+lCKfi093tXHAuFImVagLrLrYx+LJ5d22GV+myMC4F2aPVV1Lr+G5hzXaAmGK8/QaKZ74B4RxE/131S6khP9EDjI/C0Q0rnvkY/70mlKO/6n8Oo2iDMYtpp18dkVj3dhnA7P5XeRclof0CUz8e1j627OJ7vlEpT/qN0WTVmSqNgPvBWNWSqiwxnz9fkTV2DGsls7S6bGN1j6j/nfUE3SXmsQLcF/jTD5qL2XD3naeW5ugKv07VSre/sdRufcdNj/zW2UNlO+nsmt07HCqdlQWenEkKPeKglhPYkqVMZGzegCUFOTT6R3FaNFENKj7qEatknyrct8NTi/N0QLeiM4DYHc4H1/5OH4/93G+r10Va3NPeeRBP52OfDPrIhn+GDmTQhHA8dl/CWuCaJ5Kv5RWcqeAIG5cHvUALQ3ugnfvAKB59xYA6rTyuPTP9bKGLkehsj4+e049dOssBB8NKwvtmW+p9xtehkgXndJtxigcQhJ0FoA3Ru6t5JvKHSzkrltHyCh+vWc1ObyhW8bMr/g9PwzfTlNn2My6apEFFPpchF3xYgjg/uix+nELuSp0Dau8C4iWjKdZs6xrDCgzyF0L8+FqFbw1etm89Xv4SbkaI5IKUiOCoEsnd3e4nSaKKMNP444NSlwkjgfJIOwRqsMEr8uJy+ngsP2Uej16+igzHWx0iY+rj1HRfEM5OgRmSYMDxpfy4zNmc/4ipXJ9uuceiERp6wpTkhfzh39xzlzG6l59ZaHafulWRTpL/erYGz3TufbBFazbEws6FleM4TjuhEue1AdYxW7AsKZe/ylwAgcHbufn4YtZ7FiHs2MPO2d91Sx50ESRqdoinc0s3dLE041jWKYpIl8b0EfCOnxsksq/Dpapz/aUzOMjbX9V6Gr3KqUWO/bS6Y6Nh3M6BC6H4M7XFSF2WeauNRQy7jw47mZWOWZwevsjKnOibBJUxrIlNjOGAo+TAq8L4VLE3aQHwdyWwTD7VSlSCujHKSvOp8s3itE0oxlBMl2Nxyv3PVA0mkBE421NjXBuDkrGleWjFdWwN+RBfn8Luw/+oSLPT5+OG9i1dncbLZ0hCLbRIfPQvKnHBL6m1bJWU9eFhgOtWMUTvCjrpbLQQxPFtJNnkjsA79wOHQ2Em5XVtSFQij8au44+k+PocBQowjNUuzG5SsN6+NkYWH5fLEBfvxbCATqiymc2enCtUV9MuQsnXdKHI4lyt5Za3utRD/yFUrcJfaW0Fk0DYFR0Dyc5PuCoxof4o+M3ALRQSKHXhXD54kr87pLl/CZyHlOD/ySEm10l8/l+/k9oDloeJhA3XaUxqO24Tb9gvNij4lt718JLN6l1tvdQnlpqRDRBwKvI3Rdtp1kWUSb8dOzSB94lq/2fIdjkPsTw6ETs1a2UY2YoO+LYmaOonVDKQZPLmVdTwqJJ5Wz+xSks0D3f8gKPqcTnjC3hkkMnmWUNDOXeHozQFojEDQi5cPEEPrdQ3eBW0ve6HISiGvXf3MTZXT/gzfX1NFly7atLfDR3RYk4vOYAK7NqpY4gHnZTwWORQwnoN9HvPynkruAJRHDS4ijnj/lXsCFvHn/8tIhz73yXTfUdfCF0A98PX8a/GtUNKksnsFHWcHbwx7yXdxQAuxjF2aGfcH/RV9XN1rgROhrwu2I9mmmji5g2uojX1imlVVMV++wj/QGCKw8cTt7TZjBK6iqpbJIa9FQ0BongxV35ZuBU6PbRclSOvtvp4M8XL+Do6VVM0G2x/AKlnMuK8gnkjWKCo55dn7wNwB/eqGNjfTsf7EGNtL3vdNi1Agqr6QpH+Y92KD+IXs5tnScyvjyPfK8LKeGzVhc/fENP3XzoYnjuBvjb8ciP/sV5d77LHa9ugKCfVunDmd/TgG/By9p89RsTxlGqfvsyoRSvx+ngQe95fD30bdP6W1ZwhEobffM3OPQUxWUt+abt8LE2ma1yNH4KFbnvXqUOZVQW3blCqdA1j6v3Ew9Tn0W6aI+68LgctOWpXl5j2MPTa/WAoq+EqASnJUvMk6jcgTpHNVEpmOnYhnTlwdde4r+zfmV+XigCXBp9DKeeDdYqFbm7HAK/bqG9lHcyhwT/CAhKC9XvOHV0IS2dIRrbQ/F1+3XPPdTezMuh2bSPXsyMzuU85vkxodZdBHesiK3bvCX1TyElURkrCVIgO2iSRRSLLtPC7GzZy8+eGYSiZdjkPuQw/HDjIv7cwnE8+c3DmFNTQk1pHg99/RCTtIUQFOiEXl7goXZ8KX/54kJ+eNrMuH0WeJxUFnp5bvVuoppkcmW8Jzu5Ut0oLZ1hM7PmtHlqkNNb27toC7voSBilaKj85s5YquYpwV/wq+kPdTunNpnPi5qKL2xzjudP0TM5MfRrKqpG4y+ZyVfET/jT27F0smnjRvNQ9GicuoXhqZjEBzcey0dyKluj5eBwsVFT2TOvBdUDgCevhroPaXOUmqQ0r6aEGdVFBPWqjF84PGa1bNR7ArjziGqSlaHxsQbrec1UTac9bwzLdga46mh9UItui7wXVfVrPE4HJ88dw9+/vJhzF47jlnPmUjf2BH4RvpCS8moCPtXOGW//DwAr9oT5zsMrWVavM9bmN9TEK0WjCYSjSBzcHz6K+pCb8WX5FOhB9n9/VMdmaQlar38R6j4gvPQf+AMRlVEV9NMS9eEsUOTerWaJjve0WQCMd9TjrYilizodAiEEongMK+T+FAWVf/ye9zCovRD54d1Ud35GRDp4ZafbnLD655GLAUGrzNfJXU9J3LVC/W/WYx3bVXlqZp5hZq74oy6qCr1MmjYXgDbp4/FPdLsjr5SoJuOVu0sfIGaJK2yLlJl1fMKVs6ByKhuj8dlVxsMLoB2fInengw6pttsciD0sTps3hksPncT+VYU0dYZobA8mKHdF7iLYygZZw+2TbuPSyA2MEi1U7Xmbhk0fE5EO6kvmQJN+7pEg/OPM+IlmdM89qI9MLhaddLlLVXub1HeXLztwDNKE3Ta5DzGmjVY3jOF/Ox2ix3o1+frNb1gyJ86uNrNjDAghqB1fwsd16qapHR8/j+gU3U7Y6w9S4FVK6nMLlc/84ifJ89TL9clJGjuCpqJvo4BVnclV4//lXcyvw59nD5VoONioVTN1dBHlBR62NXUSimo8ftWhXHHkfpx/oCKcQ/fT9zV2PqOK1Q25osXHxUV386tNqiv+gb8c7aRfqmJiWoRWCqko9PDjM2bzlcMnM2OM+j7z3E7OWhAj8E2aPgmDO5+2rjCfSktOvO7rvzbhG1zZeglLplZyVq3u/+vVHN8IKuVvkA2otMgLFk/AVTaBv0RPp6rYx57qI3k3Oiv2W3jyWbG9hWaZEPQsGkNXOH6Q0uTKAvPh/diyOrbLUbHJJPSRme6dH1JMO2Mb3oady2mNevAUqh5KBz42adU8Gz2QZlFGZ9Fkrjl2Ksu0aeYxCkfF8rmNa86YMtLrVxbKRsbDrLMQ0SDniNf4lElsaonyYPRojgz+1nxYNGt5KvW1rU7FVho+Uzn8BsFpYVViYuIh5jHbwk7KCtzm6OQQbrPukfSVoEmJM4nnbp1UZGNAV7tAy8TjAahvD/Jd7w/ZdMgvuj3kJA4KfUq5G8HvraFY7Kd2fCk3nzGb8kIPgbDG1qZOM6C611EFHQ1owQ7cMkSbzOcvr29iWWQyQemi2L8B0bCOLbKaHa4JsXNv2gybXovV9gFzEFPQE7tnIj71203oiOXsH9g9ES0jsMl9iPGnixfw+/NrTRugNxg3f08zQQHmA6LI62JKonKviKmS0jw3h0ypMP3jlz7Za1pF1qwF42HS1B6iWbdlHAJ2NCevRV08fhZ3RM+iriX2+bRRhWbGzsSKfOZPKOP6k2eYCvikz1+pCoAt+S6gCqu9+Mke3t7jpl0fWBOOSvbOvBRO+61qT0BS7HNzyaGTmF5dxPRqZZFMKM83B3MB7PXqRO/20doVZousJiDdRHwV4FU3+u/XFNAw6lDu+uKiWCbTkdfTTj47UFk9Vs/dgNGrqSr0sWjBQu6a8gfzs6k1ymarqEy4YwtHE0joHc0cU2wq94b2ECHcnFjwMD+JfNFcR0iNM53vcEPLzQA0yyJ8xUoJduLlmNBvuTL8LX41+wnyv7WcU+ZW00nMSy+tjj3UjIlmqoq85LmdCD2zZ320GsYvRiIoEl3sLT0AUOMptlp6E01RyzV7wAUqnXX7+zHlDiqltnqeqgAKtIUdlOV7THIvpd1U0wFnIVFN9pgto7ny2doe+113TjwLUKO2N5UcSuiAL7BFKhX/VPRgVrnm4BDqYd/SGTbJvd6IwYDZ85utZ5v94r+fEvGo1xvERJBRPlurrKf8YkXGwuFiu6OGis5N5LWsZ72sYUt0lArah7tisYa6D+H5H6jejRYlooHD7aONQn4ZvoCoT7dZtSYiDvU9HFBuK/cRgdJ8D2fNr+l9RR35enXJisLUc7gCzNPTKOeNL4nr5gKU6LVtDhhXwu0XzecX58w11VsoqjFXt4QmWUbQGgTW2BGiqSOEyyGoKvKaA64SMUe/UczZ5oFp1UWmxWTEDkDFHS5YPAGPxwOLLzOH/FeX+PAHYhe60Z4dLZ20TDmdb4au5sctJ1OcF4spzKhWRD2+PP5hGS5VZCJdeTR1hoji5FM5kY6iSeq8Ixqf7GpjydTK+Kyio2/g7OLYxBnJyP3IaaM4dd4Yxpb6GFXk4+9fXgwHq4yXGZPUb3vI+ISHsTtfFeCyYHSx16weCmrcwsbGAKujqo3ULKLDXcENrgdwEWXnoT/hj5GzyC9WHq5Bkv932UH87JwDwOEw93cyt3Ga9hvy82K/qTGw7mtLJvOrc+chLnmK+2puoiUswFeCv1RZUXn7Wabxs6A+bAnAHnEdmrsQVj0WU6+gekVCwBI1iUgk0KHKb+ijiWeXBPnemQvN/Wky3pYx7MoAHoLSRSh/FNubA2wSE9iijabJoch2W1MnE8rzKclz86E2g4+0/bk6fA1f0m5SgXEh2OsPmCWbjYFngCkCjphayeLJ5bQFIiycrno4Rs0Z7dOnATj6gKnMGlPMI1ccQn3eZCYE11PcVcd6WcOaoHrI0rwlVsF053J494988ver0KRGWArcTgd/OeRl/hw9A78jlum0Jm8BAFWONMsZ9xE2uWc5ChJsmVQ4YFwpToeII1Er3rvhWO6/7GBmjy1hbGlenFr66uGT+crhk/nCwbE0ReN4je1BNuxtpzTfQ0mem5A+J2Vie+aMi7eCQFlQRlGq6dVF3T5PxOiECVCM93XNXexqC/K0dggNlJiDvwBGFXmZXFkQs7ZOuRW++ASFpVW0iGJW7glxzQMq8Ped8BW8MeMm/IEwn+3xE4poSS0xI9gNMbKxYu64Eu64aEF8WdkTfgaXvcqxSw7nuydMY/pxl/I6C3lm7DXq88JRdIWi5sQtHpcDIQT53tiD5fjZSoF+Kieq6dnGH8R/Ky8lXwRZp41j6ahz2U0FxWWK3A2FXl7gMQnSCKZ/GqikrdBSHMuCGdXFnH7AWKjcn88qjzfLD2wvVIp92sJjk04n2RHWH9yHXsMr26M81rUAbeWD0L4bqZdc6NJH+26ZchHXhS/nzvYllOfHbJnq2Udy+KxJAOwOepVyj7NljNdqcvIO7yh2tHRx27S/c1zo1/o0lVF2tnYxoaKAkjw3P4p8mYtCNwIqRmR8x3v9QVO576XUPIZB7kIIfvm5eXzz6P1ZsORkthYt4E9dx7PZOZlZa28HYPL4sfz3f5Ywf0IZTflTKJfNOImyXhvHR379Xmvc2G0O1qbOCFJT9erdTsFJs1UMyBJ64kG/+r4HKx2yex1TG1kFY9KPil7IvazAw8NfP9j09BNhlC6w4tJDJ+FyCE6ZGystUDu+lHBUUprvQQj4/cvraekM8/UjprBsayw9b0yJj6aOEGNKfOxqDTCzuhinQxDVJGfPr+HQ/SqYXFlAjT6q9sCEUbdJ26iT+aSKfE6cXc35B47nmN+8zvamTjN3H4gb4CWE4Llrl+B26ES7+DIARn+8in9xCnsDldR1qd7GJjmWq19sZ+FnH3LOghrzfBNhjWm4nd1JLikcDqhZQDGYk6X/suzHVLu9HHT+CZz9ZIjtze1MrMjHH4wwXv9erKOWDfvMTz5XO37Anw6/hEc3r6Us+gr/jR7EqF0qVbW0XFlGRpDRWlGxwLI/4/uM+spwBpJPqlLoc+EPRNA0yZMF5/KAqOSnYyezX1Ud6/b4KfK68OsP6H+HD6V2bAEnH3EjW5bu5tnoUZznegOAvVWHMHrbM6wNlNGxvgGJ5JHoUQCU5HtUpcyrl0PJeIQ+qcj2Lk83W8b6er02DpdLpaweMKGCJ1buMYPLUsLE8nx1LTi9dEVj8QxjsJ8/EKFdL0nREKfcYw/lyZUFfPdEFYh/ZuFf8T+3jms7v8x/vP8PgLziWIaYv2g/0DMXX9QW4tAk0uNC7FiqlLunyJwOcILYi5CSYFTicjqYU1PMjOoivnLwDNDrsL0amgU+bHLfV2HYMuW9eO4ACyf2TqBW3HzG7G7L5luUf1m+h6aOEAsnlvH9k2bwtX+o0XR5bielutVz+P6VvL2hgVFFXsryPTS0B5lSWcB5eg7+1w6fzKH7VfQ6yQmoBwbA1NFF3HCKygiqLvaxuaHTtJEA6prjh4EnBpiN7W7tOiPpcZZtbUYAZfnubiUd1P7UzS9EPNn0FWNL86hr7uT98FS2N6sJH8oLPGxt7OTYmUql+/S253uccQ/g/3bOpN1dxpbmID8puoltTZ0csUulEFYU56N5iujoUutbU1zdTgcel4NQRGNatYqrOK79mAU3P5O0jVMqCwhFVVDxvcY8CsaejhCCGWOKWLfHT3mhB38wQmm+m5bOfL619RBG7+igIxjhQzmD6z3Xc0vNO7xd+QXmbFnBky0T+fvd73P8rFg2i1EhlQq9J+Fw0eKp5oP20QTR4gYxWUdxXxT+AYc7KoFG8yHsD0TYptdcn1SZjxBqoo+G9ljFUiOB4MhpVazdOIH1YhIBS5G2ZKO/AbMdK+X+LAn/kdPz1/C9mkXm581Vi3lv40x+qX2JSdWVrN3tp6W8lvp3n6KmLJ+C8Yth3vksffsFFux5DIeQaDiYOaZYFyF6TUWd3BuMEbJ9md2qD7BtmSzHvHElfPv4aRw1fegrZ3bpHu3Jc6pxOIR5A50we7SpOK88aj/evv4YHA5h9i5KLb0Ml9ORFrFDzIYxUjdBBWK3NnawqzU2e006hDs6SU/FiqVbmzll7pg4MjFgkLvb6Uj6ebqoKfWxo6WLTfUxT3XBhDIe/vohfP8k5W9Xl/hYMrWSe7+82AyyG8dft9vPnrYgiyapB+6nu9rwuhwUel3IvAraUfZafsJI5JCeGjpDDzYLX7E53WIijKDiqh2trNvjN7eZW1OCQ8DoIvU9HjN9FHNr1Lqf7fazW59X9cG2eWw85QE+CIzjhNCveWyLOocPtyjCOml2NV86ZGLcMXE4eOPUV3kosoRgRCOJ86VDsHJHK0Ko4LPTIfAHwmxtVAPGJpSr66QkLz69eIp+/fzliwu59oZf8t2KO+L26ktB7larcXu0nHfLTlc9Mh15JVVcEPoRH0Umcvj+StG/K+eyf2Qj+Q2rVFzhgPN5OzLdrMB60IzJnHHA2LjjRI76IV8OX0dpYQHSWzxoyt0m9yyH2+ngmmOnxnW3hwpdYUXuxkCrzy0Yx/TRRfzs7Llme5R9owiwrEApSCNDpq8wlOskS3bPpIoCtjR2sqctQFWRl1+fO4/fnV/b+74S/PsCCwEumljGuLI8rj95RuJmQKwnYFXE/cHY0jz8gQgr62JlEfLcThZPLjcfUB6Xg39+9SAWTy5nTIkPh8Akjtc/U4OzDpmiAnf1/iCVhV6EEERPv43bImdTkudO+QCaOSZm0Z1ZO5b9qrqXVZ46uhCXQ/Dsql0EwpqZWvqFgyfy4OWHMKpYKd7ZNSU8+c3DKMt3s25PO3vagpQXeHA6BA99uN2sqd6mB8RbOsPkuZ38+QsLTCVthVE6A+iWAGCFPxBhfJnKhCrSLaStTZ3ke5xm0L8030Oxz2XGg4wyET63Gv9RlmBpWmMqVnxuwThe+vYR5uQ6VYXxveVSy3V94ORyCr0u/q9hPxxCFYgOFo1j0f++xNO7YhbQIed8s9txXEddx5aywzlyWhUiv2LQRqnatoyNlDhgfCkrt7eYN+clh07ikkMnAZhBKysBGumaBsn3FbPHlvD9k2Zw6rxYDGBiZT4NelC3uthn2j29ITHGUJrvYWKFm6aOEPd8+UA0TcYFZq1w6T77kv1T1LBPE4YSf3tD7OZNrPdjRZHPzX1fWcyE8nxeXruX1/Q65fPGlVLoddEejJhZU+79jmCL6GCcL/UtbI2//OGC+UnX8bqc7D+qkGdXqwFNM3Xl7tMfQg8vVWWT8z1OhBBMG13EZ3v8hPUsq0Kvi4c+3K6qHCZgdLE35YNnckUBkyry2dLYGVcK2wqPU42i3l8vsGdMKN/cGWZCeb6575I8N6X5HvPBYu35QXexkUq5Ox2C/UcVMbY0j+bOsKrvb4FhRQIcNb2K/UcV8vb2SfzBdQ5HldYTLjiUhvZmWqkm6vTiPOSq2MQtCXjgsoNVPG39D+NKIGcSNrnbSIkHLjvI7OIn4ugZowhF44NhBqmX9VO5Ox2CK4+Kz/AwgoxLtzZz3MwkNd9TwLB4vC4HmpQU57l56urD0aRMmt5oxSe6t33MzFE9rtcbjAyhLgvxGZZLKiyZWoWUkjElPj6ua8UhlDV16twxPLR0O5peXlkIQYHX1WPvItXDKxEzxxSzdrefQq+LqaPjVbYRfDSsn+nVRTy+fAd5Hiczqov4/KLxPLNql3luQcv1MqootTXmcAhe+c5RdIQi3dp5/ckzmF5dxJf/rmrXnH6AetgXed1srO/g011tpsgAlRhQ7w/ynUdWAt2rp5YXeHAItXxrY6cZ50iFMSV5rNnZ1o3cjfO58qj98LqcTBtdyIrtLfwuci7vFpezuLkch2jmo5tPxenaCc7U9GqKj7nn9tiWgcAmdxspke9xkYqnj5o+iqOmx5OfEfTtLW2zL5hosWiqS3oPKhso9rnIczupKctD0yQleS6cDoGT9D30JVMHFueYNrqIKVUFbKqPzbzj6YXcQRH3EVOreGjpdsbrg7OuOno/Hlq6nYhlHEGBxxmXRWTg9+fXxj1QesMFB45HSsnXlkzppmoNIjSCkNNGF+EPqqkhRxf7WDSpnG8evT9/fHUDR08fxXOWkriGpZMKDodI+gC64sj4B/zpeqmMQ/ar4O63VE79RQfFBmcdMU39Tm9vaOD5Nbu7Pby/eMhE5o4r4ZApFXy0vaXX32BsqSLeRHKfNbaY565dwnS9R2TtGe31B/lgSxOzxhbHZUANJ7KjFTZGBA7fv5LVO1p7TdvsC6ZUFZjplmNK0hvVC4oga8rymFiez3mLxplZR+ng7ksOZMPe9gF77gBfO3wKNz6+immjC/lsTzutneHeNwKOnK7I3QgOTqwo4G9fWsRki28+oSK/mwUB9GmQHMBBUyo4SPf1E2GQvfH9HbJfbL1Reu/ouydO58KDJrB6RyvPrdnN+PI8tjd1dRu30FfcfckiKgq95niC606czkfbmqks9JojrK34bYpYzMSKAlMknDi797H+xnVWWdj94WQEnAHTLgLY0xpgZ0sXFy6e0G2b4YJN7jYyhsWTy5PWoR8IfG4nz3/rCJ5auTOtG9OK337+AAq9rqQBvZ4wubIgKWn2BxcuHs/cmhLe39zI/z7zqVlhszcctn8lLoeIU4fHzYq3pe798uIBpWqmA8OWyfOo//tVFZLvcdIZisYFHGtK84hENZwOwSlzxvCXNzYxqij9nlYyHJtgw/ncTh678lCiCZPJZxrG2Ize2j+3poSSPDdza0p4S4+rpDOeY6hgZ8vYyHoU+9xcfNDEpEqqJ8wbV9pnYs80hBDMHVfCeYvGc9zMUVx+xJS0tivJc/PwFYd0syis8LmdvcYPBgpDuee5Yzrw2uPUIK3EMQITKwpY9sPjTPVqtdQyBSFE/MjgQcAJs0bz87PnckAvKbwVhV5W3nQCZ9bGUh2NtNVsgK3cbdgYApTkufnbJQf2aZtUpSSGEl53bJCVgcuWTOHYmaOTWiOl+R5K8z08d+0Spo3qveRENsLndsZ5+r1hlGVkdU9B5KFGvx+BQojxQohXhRCfCCHWCCH+R19+sxBihxBihf53Suaaa8OGjaHEIVPK9SJpMZUuhEhK7FbMqC7uMX99JMGwbxZlkSUDA1PuEeA7UsrlQogiYJkQ4kX9s99JKW8dePNs2LAxnNh/VBF3XLRguJuR1RhXlkexz9WnVN2hQL/JXUq5C9ilv/YLIT4F+hamt2HDho0cR5HPzYr/d0LW9VQyEpkQQkwC5gPv64u+KYT4WAhxjxBi+I1DGzZs2BhEZBuxQwbIXQhRCDwGXCulbAP+DOwH1KKU/W9SbHe5EGKpEGJpfX39QJthw4YNGzYsGBC5CyHcKGK/X0r5bwAp5R4pZVRKqQF/BRYn21ZKeZeUcpGUclFV1dBXPLRhw4aNkYyBZMsI4G7gUynlby3Lx1hWOxtYnbitDRs2bNgYXAwkW+Yw4IvAKiHECn3ZjcCFQohaQAJbgK8P4Bg2bNiwYaMfGEi2zFuQtArTf/vfHBs2bNiwkQnY5Qds2LBhYwTCJncbNmzYGIGwyd2GDRs2RiBscrdhw4aNEQib3G3YsGFjBMImdxs2bNgYgbDJ3YYNGzZGIGxyt2HDho0RCJvcbdiwYWMEwiZ3GzZs2BiBsMndhg0bNkYgbHK3YcOGjREIm9xt2LBhYwTCJncbNmzYGIGwyd2GDRs2RiBscrdhw4aNEQib3G3YsGFjBMImdxs2bNgYgbDJ3YYNGzZGIAaN3IUQJwkh1gkhNgghrh+s49iwYcOGje4YFHIXQjiBO4CTgVnAhUKIWYNxLBs2bNiw0R2DpdwXAxuklJuklCHgQeDMQTqWDRs2bNhIgGuQ9lsDbLe8rwMOsq4ghLgcuFx/2y6EWDeA41UCDQPYPlswUs4D7HPJVtjnkp3o77lMTPXBYJF7r5BS3gXclYl9CSGWSikXZWJfw4mRch5gn0u2wj6X7MRgnMtg2TI7gPGW9+P0ZTZs2LBhYwgwWOT+ITBVCDFZCOEBLgCeHKRj2bBhw4aNBAyKLSOljAghvgk8DziBe6SUawbjWDoyYu9kAUbKeYB9LtkK+1yyExk/FyGlzPQ+bdiwYcPGMMMeoWrDhg0bIxA2uduwYcPGCEROk3uulzgQQmwRQqwSQqwQQizVl5ULIV4UQqzX/5cNdzuTQQhxjxBirxBitWVZ0rYLhdv03+ljIcSC4Wt5d6Q4l5uFEDv032aFEOIUy2c36OeyTghx4vC0ujuEEOOFEK8KIT4RQqwRQvyPvjznfpceziUXfxefEOIDIcRK/Vx+rC+fLIR4X2/zQ3ryCUIIr/5+g/75pH4dWEqZk3+oQO1GYArgAVYCs4a7XX08hy1AZcKyXwHX66+vB3453O1M0fYjgAXA6t7aDpwCPAsI4GDg/eFufxrncjPw3STrztKvNS8wWb8GncN9DnrbxgAL9NdFwGd6e3Pud+nhXHLxdxFAof7aDbyvf98PAxfoy+8ErtRfXwXcqb++AHioP8fNZeU+UkscnAncp7++Dzhr+JqSGlLKN4CmhMWp2n4m8A+p8B5QKoQYMyQNTQMpziUVzgQelFIGpZSbgQ2oa3HYIaXcJaVcrr/2A5+iRovn3O/Sw7mkQjb/LlJK2a6/det/EjgGeFRfnvi7GL/Xo8CxQgjR1+PmMrknK3HQ04+fjZDAC0KIZXo5BoDRUspd+uvdwOjhaVq/kKrtufpbfVO3K+6x2GM5cS56V34+SiXm9O+ScC6Qg7+LEMIphFgB7AVeRPUsWqSUEX0Va3vNc9E/bwUq+nrMXCb3kYDDpZQLUNUzvyGEOML6oVT9spzMVc3ltuv4M7AfUAvsAn4zrK3pA4QQhcBjwLVSyjbrZ7n2uyQ5l5z8XaSUUSllLWq0/mJgxmAfM5fJPedLHEgpd+j/9wKPo370PUbXWP+/d/ha2GekanvO/VZSyj36DakBfyXWxc/qcxFCuFFkeL+U8t/64pz8XZKdS67+LgaklC3Aq8AhKBvMGEhqba95LvrnJUBjX4+Vy+Se0yUOhBAFQogi4zVwArAadQ6X6KtdAvxneFrYL6Rq+5PAl/TsjIOBVotNkJVI8J7PRv02oM7lAj2jYTIwFfhgqNuXDLovezfwqZTyt5aPcu53SXUuOfq7VAkhSvXXecDxqBjCq8C5+mqJv4vxe50LvKL3uPqG4Y4kDzAKfQoqir4R+MFwt6ePbZ+Ciu6vBNYY7Ud5ay8D64GXgPLhbmuK9j+A6haHUX7hV1O1HZUtcIf+O60CFg13+9M4l3/qbf1Yv9nGWNb/gX4u64CTh7v9lnYdjrJcPgZW6H+n5OLv0sO55OLvMg/4SG/zauD/6cunoB5AG4BHAK++3Ke/36B/PqU/x7XLD9iwYcPGCEQu2zI2bNiwYSMFbHK3YcOGjREIm9xt2LBhYwTCJncbNmzYGIGwyd2GDRs2RiBscrdhw4aNEQib3G3YsGFjBOL/A7EwdikUzSKiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# 获取训练和测试误差曲线\n",
    "num_epochs = 300\n",
    "models = [LinearRegression(), MLP(), MLPOverfitting()]\n",
    "train_losses, test_losses = plot_errors(models, num_epochs, train_dataloader, test_dataloader)\n",
    "\n",
    "# 绘制训练和测试误差曲线\n",
    "for i, model in enumerate(models):\n",
    "    plt.figure()\n",
    "    plt.plot(range(num_epochs), train_losses[i], label=f\"Train {model.__class__.__name__}\")\n",
    "    plt.plot(range(num_epochs), test_losses[i], label=f\"Test {model.__class__.__name__}\")\n",
    "    plt.legend()\n",
    "    plt.ylim((0, 200))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "从上图中可以看到，欠拟合的训练和测试误差曲线都呈现出较高的损失值，这表明模型在训练数据和测试数据上的表现都不佳，也就是说模型无法很好地拟合数据。在正常的情况下，训练曲线和验证曲线通常会呈现出较低的损失值，并且损失值随着训练的进行而逐渐下降。而过拟合则是在测试集上的表现较差，出现不稳定的情况甚至随着训练次数的增加反而逐渐增大。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 广而告之：如果你对实战感兴趣，比如上述代码的深度分析，如何调参等更加进阶话题，欢迎入群讨论（微信：gengzhige99），请告知“我想选修梗直哥课程《深度学习必修课：python实战》”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Next 5-5 正则化](./5-5%20正则化.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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